A man has Shs. 800,000 to be distributed among feeds, medication, and water supply in the ratio 5:3:2. Calculate the amount for medication and the amount he will pay for feeds in the third installment

The ratio for feeds, medication, and water supply is $5:3:2$.
Total ratio parts $= 5 + 3 + 2 = 10$.

Medication corresponds to 3 parts of the ratio.
Fraction for medication $= \frac{3}{10}$.

Total money $= \text{Shs. } 800,000$.
Amount for medication $= \frac{3}{10} \times 800,000$.

The amount of money available for Medication is $\boxed{\text{Shs. } 240,000}$.

Feeds correspond to 5 parts of the ratio.
Fraction for feeds $= \frac{5}{10} = \frac{1}{2}$.
Amount for feeds $= \frac{1}{2} \times 800,000$.

Total money for feeds is Shs. 400,000.

First installment $= 40\%$ of total feeds money.

The first installment is Shs. 160,000.

Remainder after first installment $= 400,000 - 160,000$.

Second installment $= \frac{2}{5}$ of the remainder.

The second installment is Shs. 96,000.

Third installment $= \text{Remainder after first installment} - \text{Second installment}$.

He will pay $\boxed{\text{Shs. } 144,000}$ for feeds in the third installment.

Divide 43 by 3:
$43 \div 3 = 14$ remainder 1
$14 \div 3 = 4$ remainder 2
$4 \div 3 = 1$ remainder 1
$1 \div 3 = 0$ remainder 1

The PIN is $1121_3$.
The actual PIN the wife will use is $\boxed{1121}$.

Number of chickens ($C_1$) $= 300$.
Number of days feeds last ($D_1$) $= 20$.

New number of chickens ($C_2$) $= 300 + 100 = 400$.
Number of days feeds will last ($D_2$) $= ?$

The total amount of feed is constant, so $C_1 \times D_1 = C_2 \times D_2$.

The same feeds will last for $\boxed{15 \text{ days}}$ after buying 100 more chickens.